1. (a) F ormalize (using a decision tree) the following decision problem, known as Pascal's wager (the same Pascal as in Pascal's triangle and early developer of probability theory): God either exists or He doesn't .. . It is abundantly fair to conceive, that there is at least a 50% chance that the Christian Creator God does in fact exist. Therefore, since we stand to gain eternity, and thus innity, the wise and safe choice is to live as though God does exist. If we are right, we gain everything and lose nothing. If we are wrong, we gain nothing and lose nothing. Therefore, based on simple mathematics, only a fool would choose to live a Godless life. Since you must choose, let us see which interests you least. You have nothing to lose. Let us estimate these two chances. If you gain, you gain all: if you lose, you lose nothing. Wager, then, without hesitation that He is. (Pascal, 1660) (b) Is the argument convincing? What, if any, problems do you see with his argument